What constitutes veteran status? I was in the National Guard but don't really consider myself a veteran.

Where are you seeing a question about being a veteran?  In My Info you are asked if you are active duty.

In my state return. In the federal return it asked if you served and it includes national guard and reserves but the state one just asks if you are a veteran. I said no.

I am no authority on military questions but according to this you are a veteran if you served active duty and received an honorable discharge.

https://va.org/determine-your-veteran-status/